derivative 2x-log_{10}(x)-7

解

導関数

2 x - lo g_{10} (x) - 7

- \frac{1}{ln ( 10 ) x} + 2

解答ステップ

\frac{d}{d x} (2 x - lo g_{10} (x) - 7)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x) - \frac{d}{d x} (lo g_{10} (x)) - \frac{d}{d x} (7)

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

\frac{d}{d x} (7) = 0

= 2 - \frac{1}{x ln ( 10 )} - 0

簡素化

= - \frac{1}{ln ( 10 ) x} + 2